AmericanLongRifles Forums
General discussion => Black Powder Shooting => Topic started by: David R. Pennington on June 08, 2018, 04:38:37 AM
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Has anyone ever presented a mathmatical formula for determining optimum twist rate for prb barrels? I have heard a couple raw theories, but seems like a good math problem. Typically smaller calibers shoot better with faster twist etc.,. Should be some mathematical equation to relate ball weight or size to rate of twist. Would you need to take barrel length into the equation? I heard one maker touted 3/4 turn in your barrel length?
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You might want to consider the velocity you will be pushing the ball with too
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Google Greenhill Formula.
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L Akers has it . (Above)
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http://kwk.us/twist.html Here's a link to a formula i found on line. the greenhill formula isn't perfect for roundballs and velocity is important. with the larger calibers you might need to balance optimum twist with just how much recoil you're willing to put up with.
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Note that the Greenhill Formula was low velocity bullet oriented.
The twist # that is the suggested from the formula is the or very close to the SLOWEST twist that will work - it is not the optimum.
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The formula I had drilled into me was, "not too slow and not too fast".
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I remember reading some articles in The Buckskin Report and also reading in John Baird's books, 15 Years in the Hawken Lode and Hawken Rifles, The Mountain Man's Choice. John had shot some original Hawken Rifles and had some fantastic groups at 100 yards ( 2 inches or less). Those guns were all 1 in 48 twist, and were 50 and 54 caliber rifles. I have always favored barrels with a 1 in 48 twist, but those are almost impossible to find now.
Maybe Rice will cut those on a special order basis, but I don't know.
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There are a lot of custom barrel makers who will cut what ever rate you want. Rayl,Burton,Carpenter to name a few.
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Bobby Hoyt as well. Just thinking Rice because their profiles are common with a lot of stock makers. Don’t care for precarves , but want the barrel fully inletted on a swamped barrel. Of course a straight barrel is always an option. Just been spoiled by swamped barrels as that is all I have used the past 20 years.
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Rice lists 1 in 48 twist for .32 and .40 caliber barrels. So they can definitely rifle a barrel with that twist. I do believe that you will pay a bit extra for a non standard twist rate for larger bores.
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There are a lot of custom barrel makers who will cut what ever rate you want. Rayl,Burton,Carpenter to name a few.
Who is Carpenter? Haven't heard that name before.
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I've been rifling my own barrels since the 70's using Greenhill's formula ( which was actually developed for artillery). For a round ball, the formula reduces to 1 turn in 150 calibers; ie for a .32 the formula is .32" X 150 = 48"--Rice's twist for their .32 as stated above. A round ball does not need a lot of rotational velocity to stabilize. The first barrel I rifled was a .43 caliber and had a 1 turn in 96" twist (I hadn't heard of Greenhill at the time) and is supurbly accurate. It has been stated that velocity needs to be considered also ( true) and that is directly related to powder charge. The faster the twist in a given caliber the more particular will be the "optimum" powder charge ( velocity). I have found a slower twist is more "forgiving" of powder charge ( velocity) without sacrificing accuracy. The slower twist seems to give a wider "optimum" window.
To answer your barrel length question, David, the barrel, regardless of twist rate, has to be long enough to burn your powder charge, no matter what amount that is, before the bullet exits the muzzle.
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and then of course there is Forsyth Rifling which applies to large balls allowing large charges.
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Jim Carpenter, St. Maries, Idaho. One of the better ones. 208-245-3693
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and then of course there is Forsyth Rifling which applies to large balls allowing large charges.
Although Forsyth rifling entails more than just a slow twist, I found it interesting that the twists he mentions in his book are very close to what Greenhill's formula gives for the calibers mentioned.
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I remember reading some articles in The Buckskin Report and also reading in John Baird's books, 15 Years in the Hawken Lode and Hawken Rifles, The Mountain Man's Choice. John had shot some original Hawken Rifles and had some fantastic groups at 100 yards ( 2 inches or less). Those guns were all 1 in 48 twist, and were 50 and 54 caliber rifles. I have always favored barrels with a 1 in 48 twist, but those are almost impossible to find now.
Maybe Rice will cut those on a special order basis, but I don't know.
On Thanksgiving Day of 1967 I finished and tested the only "Hawken"I ever made.
It was a Bill Large barrel,34"long and 1-1/8" ATF and .54 caliber with solid bolster breech
and a turn in 57".I used a soft lead .535 ball over 100 grains of DuPont 3fg and it would
do under 2"groups easily**. It was an 8 groove barrel.I was 31 when I did this good shooting and now
I doubt if I could do anywhere close to that with the sights I had then that were copied from an
original J&S.Big differences between 31 and 82 and no practice shooting for years. Bill made a lot
of 1 in 57 twist barrels and some even with Pope style rifling that were much in demand.
The late Don Brown told me of 58 caliber barrels made as an experiment for his Alex Henry copies
with rifling that looked like the splines on an input shaft of a car transmission and using 120 grains
of 3fg got over 2000 FPS and with good accuracy.
Bob Roller
**100 measured yards on a gun club range.
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In all honesty, round balls (aka bullets) are very forgiving when it comes to the rate of twist but the powder charge to push the bullet for the optimum accuracy is the key. It's not about how much powder you could use or the rate of twist it's the perfect powder charge to match that bullet size and rate of twist.
The best way to do it is to take the weight of your round ball divide that in half by grains of powder and start shooting on target. Slowly reduce your grains continuing to shoot a group on target until you found the optimum powder charge. Will end up using less powder than starting somewhere in the middle and then either working up or down.
Darrin
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and then of course there is Forsyth Rifling which applies to large balls allowing large charges.
Forsyth noted 1/4 turn in the length of the barrel - that was "his" formula. He also referred to SxS rifles, with
24" to possibly 26" bls, thus 96" to 104" twists. Most singles (16 to 14bore) of that period had 30" to 31" bls.
thus would have 120" to 124" twists. Forsyth mentioned twists as slow as 12 feet, able to give adequate accuracy
to 150yards. However, if wanting to shoot further, to 200 or 250yards, a twist rate of 1 turn in 8'8" would work, if
made correctly. This is, of course, his famous 104" twist rate.
(https://image.ibb.co/hQDAaJ/Forsyth_view.jpg) (https://imgbb.com/)
(https://preview.ibb.co/e6Thpd/Forsyth_Rifling.jpg) (https://ibb.co/cZs8Ud)
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I have for some time wanted to make a 66 cal (.660 bore shooting a .645-.650 ball ) and often wondered if a 1-85 twist would work with a 4 dram load. Hoping to keep recoil down some with that light of charge.
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I have for some time wanted to make a 66 cal (.660 bore shooting a .645-.650 ball ) and often wondered if a 1-85 twist would work with a 4 dram load. Hoping to keep recoil down some with that light of charge.
DPhar could answer that, however he is on the road at this time. His English gun has a 16 bore Dave Rayle barrel. I think it has an 85" twist, shallow grooves (I think) and he uses just over 5 drams for best accuracy, IIRC.
(https://image.ibb.co/gNYwHy/DSC03678.jpg) (https://ibb.co/den1jd)
(https://image.ibb.co/gmqhqJ/DSC03688.jpg) (https://ibb.co/e5WBjd)
Also - if I remember correctly, Dave makes his 16 bore barrels (any twist you want) with a .665" bore, so you can use a full 16 bore ball, ie: .662" Lyman mould.
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I have for some time wanted to make a 66 cal (.660 bore shooting a .645-.650 ball ) and often wondered if a 1-85 twist would work with a 4 dram load. Hoping to keep recoil down some with that light of charge.
Smylee,
I would think that load under a 16 bore round ball would as the late
Tom Dawson once said "Turn a critter Arse up in the berry patch"
I had a sxs Greener 16 bore double rifle that was potent enough with 90
grains of 3fg.
Bob Roller
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You might be right Bob and if I do build such a gun I would hope your right too. The 1-85 twist was what I thought might work for a 4 dram load, I know a lot of those English bigger game guns had the 1-104 or 1-144 twists but they to my way of thinking would need more powder to reach their best acuracy so I would want to go with a smaller load to group good and still have power enough for what ever I at my age will do or hunt with it. A .645 ball should weigh 400+ grains and one person sugested startin g loads of half the ball weight in powder, ha not this old timer. Four drams (110 grns.) sounds like a good compromise for this shooter.
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The formula I had drilled into me was, "not too slow and not too fast".
There are a lot of custom barrel makers who will cut what ever rate you want. Rayl,Burton,Carpenter to name a few.
My current formula (although I used to ponder these things at length) is now "BBL maker knows best".
I prefer to let him decide-according to what the gun is to be used for. It's their business to know these things, and mine to do other stuff. ;)
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Without the caliber, and what the gun will be used for, answering your question is kind of like the old joke question” what’s the difference between a duck”.
It all depends on those two things. Big calibers can shoot well with a fast twist at close range with light charges. And, small calibers can shoot well at close and moderate range with slow twists and heavier charges. But, you have to decide what use the gun will be put to. The 1 in 48” twist was considered a universal twist because it did pretty well out to a hundred yards with most calibers.
Hungry Horse
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Without the caliber, and what the gun will be used for, answering your question is kind of like the old joke question” what’s the difference between a duck”.
It all depends on those two things. Big calibers can shoot well with a fast twist at close range with light charges. And, small calibers can shoot well at close and moderate range with slow twists and heavier charges. But, you have to decide what use the gun will be put to. The 1 in 48” twist was considered a universal twist because it did pretty well out to a hundred yards with most calibers.
Hungry Horse
RightO. Once you understand all the trade-offs, you have to decide which ones are acceptable for your purposes. There's no un-plowed ground here, and no lack of folks who might argue that their set of tradeoffs is best. Well, their set should be best-for them and their purposes. And it loops back to my first response. ;)
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Just to illustrate that almost any twist/caliber combo can be made to work if you understand the principles, I have a perfect illustration. A kid bought a muzzleloader from a yard sale, and brought it to me to find out what it would take to shoot it. It was a cheap plastic stocked sidelock .50 cal. with a 1in 28” twist barrel. I explained to him that it was designed to shoot bullets, not balls. He was disappointed to say the least. I told him that it might shoot pretty well with pistol sized charges at relatively short range. He shot with some of us a couple of weeks later, and did very well on all targets at 100 yards and less. You could literally see the flight of the balls when he shot those new cast balls out to the 100 yard target, and they had a hard time knocking down big steel targets out there. But, he was deadly on the paper targets.
Hungry Horse
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I have for some time wanted to make a 66 cal (.660 bore shooting a .645-.650 ball ) and often wondered if a 1-85 twist would work with a 4 dram load. Hoping to keep recoil down some with that light of charge.
DPhar could answer that, however he is on the road at this time. His English gun has a 16 bore Dave Rayle barrel. I think it has an 85" twist, shallow grooves (I think) and he uses just over 5 drams for best accuracy, IIRC.
(https://image.ibb.co/gNYwHy/DSC03678.jpg) (https://ibb.co/den1jd)
(https://image.ibb.co/gmqhqJ/DSC03688.jpg) (https://ibb.co/e5WBjd)
Also - if I remember correctly, Dave makes his 16 bore barrels (any twist you want) with a .665" bore, so you can use a full 16 bore ball, ie: .662" Lyman mould.
Its an 80". Shoots great with 140 g of FF Swiss .662 ball. 1600 fps. Hard or soft lead. Even paper cartridges all shoot to the same point of aim at 50 yards. Hard lead needs a thinner patch since they cast larger from the same mould since the alloy shrinks less than lead.
Bores under 58 should work fine with a 48" twist. I think most modern makers use too slow a twist for the typical Kentucky Rifle calibers. When I get the chance I will shoot a 48" twist 62 I have to see if it blows patches. Then cut it into pistol barrels.
Dan
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Just thinking out loud, but the problem with Greenhill formula for round ball is that round balls do not need to be spin-stabilized in the same way as conicals. They are inherently stable in theory, but spin does seem to help empirically. My guess is that all the spin does is level out any irregularities in the ball, which if true would lead to the conclusion that it would be best to err on the slow side as far as twist goes, since spinning too fast would cause more problems than it solves. To support this conjecture, I could point to the tradition that larger calibers intended for higher velocities typically have slower twists, perhaps because the larger radius amplifies negative effects of too much spin? On the other hand, too slow might require excessive velocity...
As pointed out above by HH, fast twists often do fine with lower velocities, so obviously there is a sweet spot, but it would seem to depend on caliber and velocity, as well as perhaps uniformity of the round ball? And as DPhariss points out, faster twist can rip off patches at higher charges, which muddies the waters.
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Actually, Forsyth quite well explained this, in his VISCIOUS circle of events. The more spin, (faster twist), the tighter must be the hold, which might deform the ball, which reacting with the atmosphere, required more twist to stabilize, which then required a tighter fit, etc, etc.
As to round balls needed less twist, that is shown quite well in the slower twist barrels available today. They do not, however embody completely Forsyth'sa principle of slow twist and really shallow grooves with very narrow lands - like the photograph I posted, shows.
I have proven, at least to my satisfaction, in my .69's 66" twist, that a tight fitting ball with produce 2" to 2 1/2" groups at 100 meters off the bags with a mere 82gr. 2F, but that 82gr. 3F produced 4" groups- go figure. I recently (last summer) discovered that the 2f load produced exactly the same velocity as-had the earlier (1986 0-GOEX) 3f produced & that 2f was more accurate than the previous 3F gave me. I then found that increasing the charge to 165gr., of 2F produced groups from 1" to 1 1/2" at the same range, of 100 meters. I suspect a 48" twist would not produce such groups at 1,550fps, as-did the 165gr. charge.
I do not know that as fact as I do not know from experience, what a 48" twist will produce in that calibre. I would, however, very much like to test an 85" to 104" twist in that calibre, if bored to Forsyth specifications. The barrel would need to be straight or minor taper, 1 1/8" at the breech. I know a guy who can re-barrel my rifle, for me.
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Without the caliber, and what the gun will be used for, answering your question is kind of like the old joke question” what’s the difference between a duck”.
This kind of misses the point of my original question. I was wondering if anyone had ever tried to come up with a mathematical equasion (where you could plug in all the variables, such as caliber, average rb velocity etc.,.) and come up with a formula to calculate, at least in theory, what the optimum rate of twist should be.
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Nothing I am aware of for round ball guns. The Greenhill Formula is for conicals.
This formula has been modernized slightly to give more realistic #'s for today's higher
velocity rifles.
Note that this formula produced the 'slowest' twist that would work for that length of
projectile, not the optimum twist.
The problem with having the slowest, barely stabilizing
twist for elongated projectiles, was that at extended ranges, accuracy fell off as the projectile
slowed.
This is also shown in Lt. James Forsyth's book, as he noted if one was shooting fairly close
ranges, a 12' twist was enough, but if wanting to range to 150 or 200yards, that an 8'8" twist
was the best. He was talking of "bore" rifles, not .45's through .58's which he though of as toys,
as they were totally useless in the pursuit of the game he chose to pursue.
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The Greenhill formula is only a guide, it was intended for use for bulleted ARTILLERY according my reading. In bulleted small arms, shooting 3 caliber + long bullets, its about 2" slower than it could be. IE if Greenhill gives a 20" twist then use an 18. For round balls? They are so forgiving that I would not worry. As I stated above 48" is very good for most calibers in use today. Remembering that this would be about one turn in the barrel of most "4 foot" (+-) barreled Kentuckys. I have never been able to figure out why modern ML barrels are twisted so slow. I would prefer 48" for everything I own other than the 16 bore rifle. Heavy balls have more rotational inertia and are more likely the "blow" the patch as they start to rotate. At 1600 fps a 48 in twist barrel gives the ball 24000 RPM. In an 80" twist its only 14400 rpm so the heavier ball is less likely to "blow" or "strip" the patch. Remembering how fast the ball goes from 0 to many thousands of RPM in the length of the barrel.
See http://bulletin.accurateshooter.com/2008/06/calculating-bullet-rpm-spin-rates-and-stability/
Another formula is MV/twist in feet * 60 it was my solution before finding this site it gave the same answer.
Dan